more comments in the binomial example

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I could use more comments in the binomial example.

For example, how does this follow? "the asymptotic variance of   does exist and is equal to .."

For example, how does this follow? "since p>0,     as  "

For example, how does this follow? "the logarithm of the estimated relative risk   has asymptotic variance equal to .."

I'm sure these are trivial to someone who can already see it, but I don't.

Also, more text about the practical implications of this example would be good. The relative risk thing at the end is a start, but what about the proportion itself? What is a concrete, real-world example?

dfrankow (talk) 16:48, 21 December 2018 (UTC)Reply

normality

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You do not need normality to use the delta method —Preceding unsigned comment added by 75.73.53.186 (talk) 01:28, 2 March 2011 (UTC)Reply

Convergence in probability to

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At the beginning of the proof, it says "..since  ..". Where does this come from? — Preceding unsigned comment added by 128.40.213.241 (talk) 14:29, 5 November 2015‎   as   since   and   Vinzklorthos (talk) 20:08, 5 August 2020 (UTC)Reply

Someone commented on the variance of the log of a rv.

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It does exist provided you are dealing with positive support  . Now the average of   will need n to be large enough for the density at 0 to become vanishingly small. Limit-theorem (talk) 20:57, 8 July 2015 (UTC)Reply

Perhaps to avoid the subtleties of almost sure convergene, it is best to insert another example with C-infinity transformation on the real line. I can do so later. Limit-theorem (talk) 13:57, 15 July 2015 (UTC)Reply
I was the one who added that comment. The support is not positive since a binomial random variable can be zero. Btyner (talk) 17:49, 23 August 2015 (UTC)Reply
The example doesn't state that it is an approximation of the variance of a binomial, rather that it is an approximation of the variance of the limiting normal distribution whose variance does exist. I'd recommend removing the disclaimer. 2602:306:3844:5400:90C5:53FB:DA9D:CDDA (talk) 21:41, 20 April 2016 (UTC)Reply
I went ahead and reworded it in this edit, and removed the disclaimer. Btyner (talk) 00:49, 28 April 2016 (UTC)Reply